Because an0⁢q+an0⁢q2+…+an0⁢qp+…subscriptasubscriptn0qsubscriptasubscriptn0superscriptq2normal-…subscriptasubscriptn0superscriptqpnormal-…a_{{n_{0}}}q+a_{{n_{0}}}q^{2}+\ldots+a_{{n_{0}}}q^{p}+\ldots is a convergentgeometric series, those inequalities and the comparison testimply that the series